NormR wrote:I don't remember off the top of my head, but how stable are skewness and kurtosis? That is, is the past a good guide to the future for these items?

Good question. I don't know the answer.

On the other hand, we have learned, quite painfully, that correlations across assets are definitely not stable over time. They increase dramatically in economic downturns.

Also, if one goes to where the math is hard, why not opt for semi-var instead of var? Perhaps that makes it too hard?

I've seen a number of papers looking at semi-var instead of var. My recollection is that using semi-var doesn't buy you much, if anything, in terms of explaining prices or returns.

I can see the attraction of using semi-var if you think that there is skewness. But again it doesn't capture the same information that skewness does. Think of semi-var as a way to describe a lottery -- it seems intuitive to me that skewness is capturing something quite different.

Isn't that just putting a behavioural argument into math speak? It doesn't really explain why.

Isn't all of financial analysis just quantifying factors that behaviourally we find important? After all, what is the rationale for risk aversion other than a fundamental human bias of not liking risk? Then we run around and try to put a number on it and call it "the price of risk".

Having lived through a couple of crashes now, I personally know that I don't like risk, although I'm still not sure why not. But as a result, I do try to quantify risk in various ways (I avoid reliance on variance or standard deviations, as I've said before).

Similarly, having bought a good number of lottery tickets, I know that I like skewness, at least to some extent. The intuition is simple. If I lose ten dollars, which I almost certainly will, that doesn't change my lifestyle one bit. But if I win one million, that will be a big benefit to me. Call it a behavioural quirk, but I think that skewness plays an important role, at least some of the time. And I think that it is a factor different from risk (or, more precisely, a factor different from volatility; once we introduce higher moments, it's not clear how risk is defined any more).

As to whether the third moment of the distribution of expected returns is an adequate measure of skewness, that is an entirely different matter, in a league with whether variance is an adequate measure of volatility.

Anyway, I welcome your comments. I'm still slowly feeling my way through this.

I recently came across this free online "book" (178 pages with 14 articles) from Russell Investments that seems to have much quality information in it - I use "seems" because I have not had time yet to go through all of it.

Inside this guidebook you will find 14 articles by Russell consultants and strategists that have been published over the past fourteen years on the subjects of risk management and fund governance. Some of the articles are short, others longer. Some concentrate on very specific questions, others cover broader ground. Together, they provide a wonderful education for fiduciaries charged with the oversight of a public or corporate pension plan, an endowment, a foundation, or any other type of institutional investment program.

As I write this introduction in mid-2010, few investors need to be reminded of the importance of risk management. Risk was not invented in 2008, of course, but it did begin one of its periodic spells on center stage. Risk is an elusive concept. It means different things at different times to different people. Stock market investment felt like a bleak prospect in the depths of March 2009 when valuations were little more than half their peak value and the possibility of further declines with no floor in sight felt all too real. Risk in that situation is both quantitatively and qualitatively different than in the midst of a bull market.

“The search for truth is more precious than its possession.” Albert Einstein

I don't actually know anything, but can risk be discussed without reference to its object? I'd think that risk is the chance that something you don't want to happen happens. You can discuss what risk of capital loss is, what risk of achieving returns below needs is...but "risk" itself is just the chance of [insert undesirable outcome] happens.

In financial literature "risk" is a four letter word that often means nothing or whatever the reader wishes it to mean.
It is partly because of this ambiguity that I keep returning to this thread - to expand and clarify understanding.

“The search for truth is more precious than its possession.” Albert Einstein

When you "derisk," be sure you understand whether you are eradicating risk—or just replacing old risks with new ones... When everyone seems to want to unload the same risks at once, it is a good idea to ask yourself whether joining them might be the biggest risk of all.

The riskiness of an investment is not measured by beta (a Wall Street term encompassing volatility and often used in measuring risk) but rather by the probability -- the reasoned probability -- of that investment causing its owner a loss of purchasing power over his contemplated holding period. Assets can fluctuate greatly in price and not be risky as long as they are reasonably certain to deliver increased purchasing power over their holding period. And as we will see, a nonfluctuating asset can be laden with risk.

“The search for truth is more precious than its possession.” Albert Einstein

A very important step that, unfortunately, almost no individual investors take.

When I was in graduate school, it was drummed into us ("hammered" might be more accurate) that no forecast or estimate should ever be given to a client without an accompanying confidence interval, or at least a qualitative assessment of the chances of the forecast/estimate being wrong. Then I entered the work force, and was told that people didn't want all that clutter -- just the point forecast, please.

Forty years later, people still don't want to know about uncertainty.

So congratulations on being one of the very few to take randomness seriously.

ghariton wrote:Then I entered the work force, and was told that people didn't want all that clutter -- just the point forecast, please. Forty years later, people still don't want to know about uncertainty.

I learned that lesson when I started reading about safe withdrawal rates in retirement. People insist on a single number like x% that's cast in concrete and guaranteed to survive, no matter what. It's futile trying to explain why that's impossible (unless you make 100/x much, much larger than they can ever hope to amass. (Even an all RRB portfolio or an annuity has its risks...))

The riskiness of an investment is not measured by beta (a Wall Street term encompassing volatility and often used in measuring risk) but rather by the probability -- the reasoned probability -- of that investment causing its owner a loss of purchasing power over his contemplated holding period. Assets can fluctuate greatly in price and not be risky as long as they are reasonably certain to deliver increased purchasing power over their holding period. And as we will see, a nonfluctuating asset can be laden with risk.

Yes. But look at what's really going on. Buffett is looking at both expected return and volatility. If the expected return is high enough, then large downward volatility is acceptable, because even large drops will still leave the investment "above water". By contrast, if the expected return is lower, the acceptably volatility is lower because then even medium drops will result in a loss.

One can argue (and some do) that the proper measure of volatility should be the semi-variance rather than the variance, i.e. the sum of squares of negative errors (rather than all errors, negative and positive). For a symmetric distribution, the difference doesn't matter. For a skewed distribution, it does in theory, although in practice the increase in explanatory power is thought not to be worth the effort.

But as I mentioned upthread, skewness seems to be an important factor in its own right, over and above distinguishing positive from negative volatility.

The more I think about it, the more intrigued I am by a four-factor model (expected return, volatility, skewness, and how fat the tails are (kurtosis). In such a model, risk is no longer identified with volatility, of course. Rather, it is a function of skewness and kurtosis as well.

I realize that many people would not find such a decomposition of risk to be helpful -- to paraphrase a judge, "I know risk when I see it". But I fear that going by gut instinct, even if augmented by experience, will only take us so far, and important risks will be overlooked. In any event, I find decompositions helpful.

newguy wrote:For skewness are all your positive results from one large trade or something like that?

Not necessarily, although that makes it more likely.

A useful example when thinking about skewness is a bond, or a portfolio of bonds. There, the skew is negative (long tail on the left) due to credit risk. There is also volatility, due to market risk, i.e. changes in interest rates. But clearly volatility as a measure does a very poor job of capturing credit risk. Skewness (one quantification of which is through credit agency ratings) is separately important.

For U.S. equities, the study found that the least volatile 10% of stocks had an average return of 12.2% over the period, while the most volatile 10% combined for an average decline of 8.8%.

“We found that in every one of the world's markets, higher volatility equals lower returns,” Mr. Haugen said. “Does this fly in the face of modern portfolio theory? You're damn right it does.”

I think that all those professors teaching Investing 101 to absorbing students should be required to write the following out 1,000 times before they are allowed to teach the next class - "VOLATILITY IS NOT THE SAME AS LONGER TERM INVESTMENT RISK"

“The search for truth is more precious than its possession.” Albert Einstein

I'm a newbie that was very graciously helped with his AA here. Been reading and learning quite extensively and am getting seriously hooked.

A point I've been tripping up on and would appreciate input on (and maybe generate a discussion if this doesn't turn out being a stupid newbie point ) is as follows:

I see a clear distinction between short term and long term risk in both bond and equities markets.

Short term risks is basically price fluctuations in response to changing yield environments and speculation.

Long term risks (at least the way I understand it) is much more a risk of return below inflation. I'm using loss of purchasing power as downside risk as that's what I perceive to be an actual "loss" of what I put in.

Price drops will be offset by a rise in yields in due time (bond term for bonds and a period correlated to the drop in case of stock -may be as long as 30+years). Eventually, your long term return will be the income generated by the asset. Your principal will "disapear" to inflation in a few decades. What you will be left with is your return. If that return is below inflation (or after tax return in taxable accounts), you are incurring a loss. In this sense, lower expected yield vehicles are actually riskier as long term investments. In this sense, bonds are (long term) riskier than stock.

It seems that markets price short term capital loss risk into stock and in doing so make stock less risky long term investments. This make any semblance of sense?

Maybe an added clarification. I'm refering to broad based internationally diversified indexes when I say "stocks". I'm basing my reasoning on the fact that, at today's prices, I can buy (for my long term portfolio) either bonds that will yield about 2% or stocks that will yield 2%+earnings growth. Of course, the stock yield is more uncertain. But, by playing around with the Gordon equation, you can "predict" that a 5% growth rate will yield long term stock returns of 7%. A 5% premium over bonds. That 5% is a "safety margin". To yield 2% long term, stock earnings would have to stay flat long term. Global business would be bankrupt in that scenario. How risky are government bonds when global business is bankrupt?

What I'm getting at is that if the expected equity premium is of a margin that to be wiped out requires catastrophic "end of capitalism" events, why are government bonds more "safe"? Why are they not, long term, more risky as their expected yields (at today's prices) are below expected inflation?

I'm a little confused on your question. Are you trying to compare performance of stocks against long-term bonds? "Equity risk premium" is compared to a "risk-free" baseline. In the US, the risk-free baseline is the 90 day (short-term) US Treasury bill. (I don't know the Canadian risk-free baseline.) The reason that short-term bonds are used is due to the stability of the return - it's practically guaranteed.

You may be perceiving "risk" to be the same as "loss" - those are 2 different concepts. Risk is the range of return variation.

LadyGeek wrote:I'm a little confused on your question. Are you trying to compare performance of stocks against long-term bonds? "Equity risk premium" is compared to a "risk-free" baseline. In the US, the risk-free baseline is the 90 day (short-term) US Treasury bill. (I don't know the Canadian risk-free baseline.) The reason that short-term bonds are used is due to the stability of the return - it's practically guaranteed.

LadyGeek wrote:I'm a little confused on your question. Are you trying to compare performance of stocks against long-term bonds? "Equity risk premium" is compared to a "risk-free" baseline. In the US, the risk-free baseline is the 90 day (short-term) US Treasury bill. (I don't know the Canadian risk-free baseline.) The reason that short-term bonds are used is due to the stability of the return - it's practically guaranteed.

Except T-Bills are not risk free. Also, they might be 'guaranteed' but they come with counterparty risk that has bitten investors in G7 economies in the past. At last check, the U.S. was only a AA credit. A permanent impairment of purchasing power is a definite probability.

LadyGeek wrote:I'm a little confused on your question. Are you trying to compare performance of stocks against long-term bonds? "Equity risk premium" is compared to a "risk-free" baseline. In the US, the risk-free baseline is the 90 day (short-term) US Treasury bill. (I don't know the Canadian risk-free baseline.) The reason that short-term bonds are used is due to the stability of the return - it's practically guaranteed.

Except T-Bills are not risk free. Also, they might be 'guaranteed' but they come with counterparty risk that has bitten investors in G7 economies in the past. At last check, the U.S. was only a AA credit. A permanent impairment of purchasing power is a definite probability.

Correct, but that's what was used as the "risk free" baseline in the data.

The Bank of Canada Interest Rates only go back 10 years, compared to the 83 year historical information available for the US markets. (Perhaps there is a better website, but RBC is the official source of information.)

It would be an interesting comparison to see if a similar risk versus return pattern emerges using Canadian bond and market historical information; perhaps that would make a nice entry for finiki. The bottom of Risk and return: an introduction - Bogleheads contains a link to the Excel spreadsheet which has everything you need to do the calculations and reproduce the charts.

Note: The bond information is not yield, it's return, which takes into account bond pricing. (The return on a bond is the sum of the coupon and maturity cash flows.) The stock market index includes dividends.

Not shown in the wiki, but it's in the spreadsheet, is an analysis which attempts to predict a 95% confidence value (Value At Risk) for maximum loss. In 2008, that loss prediction was exceeded.
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Rooster - I had trouble understanding your questions. Does the Bogleheads' wiki info help? If not, try asking again. My main point is that you need to be very careful about extrapolating historical information into the future. It's very difficult to tell what will happen in 20 years, even 5 years is too long to know for sure. "Past performance does not predict future performance." You mitigate risk by diversification.